A general proof of consistency of heuristic classification for cognitive diagnosis models |
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| Authors: | Chia‐Yi Chiu Hans‐Friedrich Köhn |
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| Affiliation: | 1. Rutgers, The State University of New Jersey, New Brunswick, New Jersey, USA;2. University of Illinois at Urbana‐Champaign, Champaign, Illinois, USA |
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| Abstract: | The Asymptotic Classification Theory of Cognitive Diagnosis (Chiu et al., 2009, Psychometrika, 74, 633–665) determined the conditions that cognitive diagnosis models must satisfy so that the correct assignment of examinees to proficiency classes is guaranteed when non‐parametric classification methods are used. These conditions have only been proven for the Deterministic Input Noisy Output AND gate model. For other cognitive diagnosis models, no theoretical legitimization exists for using non‐parametric classification techniques for assigning examinees to proficiency classes. The specific statistical properties of different cognitive diagnosis models require tailored proofs of the conditions of the Asymptotic Classification Theory of Cognitive Diagnosis for each individual model – a tedious undertaking in light of the numerous models presented in the literature. In this paper a different way is presented to address this task. The unified mathematical framework of general cognitive diagnosis models is used as a theoretical basis for a general proof that under mild regularity conditions any cognitive diagnosis model is covered by the Asymptotic Classification Theory of Cognitive Diagnosis. |
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| Keywords: | cognitive diagnosis general cognitive diagnostic models generalized DINA loglinear cognitive diagnosis model asymptotic theory of classification for cognitive diagnosis classification cluster analysis consistency |
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